Answer:
Step-by-step explanation:
I'll try to make this make as much sense as possible. If we have a cone with a liquid in it, this liquid takes up volume. Therefore, our main equation, at least at first, is to find the volume. This is because if we pump the liquid out of the tank, the thing that changes is the amount of liquid in the tank which is the tank's volume. The formula for the volume of a circular cone is
[tex]V=\frac{1}{3}\pi r^2h[/tex] and here's what we know:
r = 2 and h = 8. The formula for volume has too many unknowns in it, so let's get the radius in terms of the height and sub that in so we only have one variable. The reason I'm getting rid of the radius is because in the problem we are being asked how much work is done by pumping the liquid to the top of the tank, which is a height thing. Solve for r in terms of h using proportions:
[tex]\frac{r}{2}=\frac{h}{8}[/tex] and solve for r:
[tex]r=\frac{2}{8}h =\frac{1}{4}h[/tex] so we will plug that in and rewrite the equation:
[tex]V=\frac{1}{3}\pi(\frac{1}{4}h)^2h[/tex] and simplify it til it's a simple as it can get.
[tex]V=\frac{1}{3}\pi(\frac{1}{16}h^2)h[/tex] and
[tex]V=\frac{\pi}{48}h^3[/tex] and since the volume is what is changing as we pump liquid out, we find the derivative of this equation.
[tex]\frac{dV}{dt}=\frac{\pi}{48}*3h^2\frac{dh}{dt}[/tex] and of course this simplifies as well:
[tex]\frac{dV}{dt}=\frac{\pi}{16}h^2\frac{dh}{dt}[/tex]
Work is equal to the amount of force it takes to move something times the distance it moves. In order to find the force it takes to move this liquid, we need to multiply the amount (volume) of liquid times the weight of it, given as 1000 kg/m³:
F = [tex]1000(\frac{\pi}{16}h^2\frac{dh}{dt})[/tex] and the distance it moves is 8 - h since the liquid has to move the whole height of the tank in order to move to the top of the 8-foot tank. That makes the whole integral become:
[tex]W=\int\limits^8_0 {1000(\frac{\pi}{16}h^2(8-h)) } \, dh[/tex] and we'll just simplify it down all the way:
[tex]W=62.5\pi\int\limits^8_0 {8h^2-h^3} \, dh[/tex] and you're done (except for solving it, which is actually the EASY part!!)
use the figure to find y
Answer:
y = 3
Step-by-step explanation:
6sin(30) = 3
-3u-17=(u+8)
simplify
Answer:
-25/4 = u
Step-by-step explanation:
-3u-17=(u+8)
Add 3u to each side
-3u+3u-17=(u+3u+8)
-17 = 4u +8
Subtract 8 from each side
-17-8 = 4u+8-8
-25 = 4u
Divide by 4
-25/4 = 4u/4
-25/4 = u
The elevation E, in meters, above sea level at which the boiling point of a certain liquid ist degrees Celsius is given by the function shown below. At what elevation is the boling point 99.5*7 100°?
E() - 1200(100-1) • 580(100 - 1)
At what elevation is the boiling point 99.5?
E (90.5*)=. meters
At what elevation is the boiling point 100"?
E(100*)-meters
Answer:
Given E(t)=1100(100-t)+580(100-t)^2
Put t = 99.5, we get
E(99.5)=1100(100-99.5)+580(100-99.5)^2
E(99.5)=1100(0.5)+580(0.5)^2
E(99.5)=1100(0.5)+580(0.25)
E(99.5)=550+145
E(99.5)=695m
Step-by-step explanation:
It can be concluded that -
E(99.5) = 695
E(100) = 0
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the function as follows -
E(t) = 1100(100 - t) + 580(100 - t)²
The given function is -
E(t) = 1100(100 - t) + 580(100 - t)²
At → E(99.5)
E(99.5) = 1100(100 - t) + 580(100 - t)²
E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²
E(99.5) = 1100(0.5) + 580(0.5)²
E(99.5) = 550 + 145
E(99.5) = 695
At → E(100)
E(100) = 1100(100 - t) + 580(100 - t)²
E(100) = 1100(100 - 100) + 580(100 - 100)²
E(100) = 0
Therefore, it can be concluded that -
E(99.5) = 695
E(100) = 0
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Second to last question, Find I
50 points
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from angle I, we know the opposite side and the hypotenuse. Therefore, we should use sine.
sin(I) = [tex]\frac{\sqrt{39}}{\sqrt{51}}[/tex]
To solve, you can use your calculator and the inverse sine function (sin^-1).
I = sin^-1([tex]\frac{\sqrt{39}}{\sqrt{51}}[/tex])
I = 61 degrees
Hope this helps!
The lengths of the three sides of a triangle are 3, 15, and 16. Classify it as acute, obtuse, or right.
Answer:
Obtuse Scalene Triangle
Step-by-step explanation:
Sum of the squares of the smaller 2 sides < longest side squared = Obtuse Scalene Triangle
Express the set shown below in roster form. {x | x is a natural number less than -2}
Given:
The set is:
[tex]\{x|x\text{ is a natural number less than }-2\}[/tex]
To find:
The raster form of the given set.
Solution:
We know that, natural numbers are all positive integers.
Natural numbers: 1, 2, 3, 4,... .
The given set is:
[tex]\{x|x\text{ is a natural number less than }-2\}[/tex]
Here, x is a natural number and it is less than -2, which is not possible.
Since all natural numbers are greater than or equal to 1, therefore the given set has no element.
[tex]\{x|x\text{ is a natural number less than }-2=\phi[/tex]
Therefore, the roaster form of the given set is [tex]\phi[/tex] or [tex]\{\ \}[/tex].
Which of the following is equal to -16?
Answer:
The last one. 4.
Step-by-step explanation:
The square root of a positive or negative number can't be negative. so it's positive 4.
What are the solutions to the equation
Answer:
(0,1) and (3,4)
Step-by-step explanation:
It's the points where they meets, judging the graph, it's x = 0, y = 1 and x = 3, y = 4
put them in the equation and you'll see the the values satisfies the equation
Answered by GAUTHMATH
The sum of 3 unequal odd numbers is 203. What may those numbers be? Give four possible answers.
Answer:
71, 69 and 63
71, 67 and 65
73, 67 and 63
75, 65 and 63
Write the quadratic equation in standard form:
7x + 8 + 2x2
2x + 1 + x2
Answer:
[tex]3x^2 + 9x +9[/tex]
Step-by-step explanation:
Given
[tex](7x + 8 + 2x^2) + (2x + 1 + x^2)[/tex]
Required
The result in standard form
We have:
[tex](7x + 8 + 2x^2) + (2x + 1 + x^2)[/tex]
Remove brackets
[tex]7x + 8 + 2x^2 + 2x + 1 + x^2[/tex]
Collect like terms
[tex]7x+ 2x + 8 + 1 + 2x^2+ x^2[/tex]
[tex]9x + 9+ 3x^2[/tex]
The standard form of a quadratic equation is:
[tex]ax^2 + bx + c[/tex]
So, we have:
[tex]9x + 9+ 3x^2[/tex]
[tex]3x^2 + 9x +9[/tex]
Solve 60 ÷ 5(1 + 1(1 + 1))
Answer:
Creo que es 36
Step-by-step explanation
:D
Answer:
36
Step-by-step explanation:
Eddie is using his phone's calculator app to calculate 16,544 × 70. He accidentally enters 16,544 × 7 instead. How can he correct his mistake
Answer:
Multiply the product of 16,544 x 7 by 10 as it id the same as multiplying 16,544 x 70.
3) Consider the sequence -11 ; 2sin3x ; 15; ...
3.1.1) Determine the values of x in the interval [0 ; 90] for whichthe sequence will be arithmetic.
❤❤❤❤❤❤I WILL MARK AS BRAINLIEST IF RIGHT PLEASE HELP ME PLEASE BE CORRECT BEFORE ANSWERING PLEASE AND THANK YOU.
TELL ME WHERE TO PUT EACH POINT OF THE TRIANGLE TY
Answer:
Please look at the picture
Step-by-step explanation:
Please look at the picture I have drawn it for you
Find all points of intersection of the given curves. (Assume 0
blank.)
R= 1 - cos(Theta), r = 1 + sin(theta)
9514 1404 393
Answer:
POLE(1+(√2)/2, 3π/4)(1-(√2)/2, 7π/4)Step-by-step explanation:
Your have correctly identified the points of intersection, but you need to follow directions in your entry of those answers. "POLE" goes in the first answer slot. You may also be expected to rationalize the denominator, or provide the r value as a single term.
The points of intersection are ...
POLE
((2+√2)/2, 3π/4)
((2-√2)/2, 7π/4)
Which of these is a key feature of an experimental study?
A.
The treatment in the experiment should be simple enough for each individual in the experimental group to understand.
B.
The treatment in the experiment must vary for each individual in the experimental group.
C.
The treatment in the experiment must be applied to each of the individuals in the experimental group.
D.
The treatment in the experiment should be short so that each individual is tested quickly.
Find the lateral area of this square based pyramid. 10in 5in (in the image)
Answer:
100 in²
Step-by-step explanation:
4 triangles, each of them has area = 10*5/2
so total area = (10*5/2)*4
= (10*5*2)
= 100 in²
Answered by GAUTHMATH
The lateral surface area of the pyramid is 100 in²
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
The pyramid has four triangular faces and one rectangular base we need to calculate the lateral surface area so we will calculate the area of the four triangles and sum up all the triangles.
4 triangles, each of them has an area = 10 x ( 5/2 )
So total area = (10 x 5/2) x 4
Total area = (10 x 5 x 2)
Total area = 100 in²
Therefore the lateral surface area of the pyramid is 100 in²
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Lisa made a shirt using 1/3 m of blue fabric and 3/5 m of red fabric how many meters of fabric did she use in all
Answer: 14/15 of a meter
Step-by-step explanation:
5 and 3 LCM is 15.
3/5 x 3 + 1/3 x 5= 9/15 + 5/ 15 = 14/15
What is the point slope form of a line with slope -5 that contains the point (2-1)? Ay+ 1 = -5(x-2) B. y + 1 = 5(x + 2) O coy-1-5(x-2) O D. y 15(x + 2)? anyone help plz
Answer:
A. y + 1 = -5(x - 2)
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Identify
Slope m = -5
Point (2, -1)
Step 2: Find Equation
Substitute in variables [Point-Slope Form]: y - -1 = -5(x - 2)Simplify: y + 1 = -5(x - 2)The number of typing errors made by a typist has a Poisson distribution with an average of three errors per page. If more than three errors appear on a given page, the typist must retype the whole page. What is the probability that a randomly selected page does not need to be retyped
Answer:
0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Poisson distribution with an average of three errors per page
This means that [tex]\mu = 3[/tex]
What is the probability that a randomly selected page does not need to be retyped?
Probability of at most 3 errors, so:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]
Then
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0498 + 0.1494 + 0.2240 + 0.2240 = 0.6472[/tex]
0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.
I am having troubles finding x, need an explanation
Answer:
56+35=180 then solve it thanks
Answer:
Step-by-step explanation:
we have a two right triangle, with one side 115
lets say that the other side of the big right triangle is y
-in the big triangle find the third angle
180 -90 -35 = 55, because the sum of all interior angles in a triangle is 180
tan 55 = opp. /adj= y / 115
y = 115 * tan 55
-in the small right triangle
tan 56 = opp./ adj. = 115 / y-x
y-x = 115/ tan 56 , subtract y from both sides
- x= -y +( 115/tan 56), multiply by -1 both sides
x= y -(115/tan56), substitute y for 115 * tan 55
x= (115*tan 55)- (115/tan56)
x≅86.6685
You are walking from home to a grocery store you stop for a rest after 2/5 miles the grocery store is actually 3/4 miles from home how much farther do you have to walk
Answer:
7/20 mile farther
Step-by-step explanation:
Subtracting 2/5 mile from 3/4 mile results in the distance you still have to walk:
3/4 - 2/5 = ?
Here the LCD is 20. Thus, 3/4 becomes 15/20 and 2/5 becomes 8/20.
Then 3/4 - 2/5 = 15/20 - 8/20, or 7/20.
You still have 7/20 mile to walk to get home.
(3 A sum of money doubles itself in 6 years. In how many years, it becomes 5 times?
Answer:
In 24 years.
Step-by-step explanation:
Let the sum of money be 100 which amounts to 200 ( doubles itself ) in 6 years time. Interest on 100rs. Is 100. Putting the following in simple interest formula. You get :
[tex]100=\dfrac{100\times R\times 6}{100}\\\\R=\dfrac{100}{6}[/tex]
Now when 100 will become 5 times i.e 500 the interest will be 400rs.
Putting in simple interest formula:
[tex]400=\dfrac{\dfrac{100\times 100}{6T}}{100}\\\\T=\dfrac{2400}{100}\\\\=24\ yrs[/tex]
So, in 24 years, it will become 5 times.
he ride a bike for 15 miles oer hour how many miles did he ride
I need the answer to this
Answer:
[tex]A)\:x<12[/tex]
[tex]5(x+5)<85\\5x+25<85\\5x<85-25\\5x<60\\x<12[/tex]
OAmalOHopeO
Answer:
x < 12.................................
The function ƒ(x) = (x − 1)^2 + 5 is not one-to-one. Find a portion of the domain where the function is one-to-one and find an inverse function.
The restricted domain for ƒ is ?
Answer:
f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.
Step-by-step explanation:
The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.
* if x>1, then x-1>0.
* Also since the parabola opens up, then y>5.
So let's solve y=(x-1)^2+5 for x.
Subtract 5 on both sides:
y-5=(x-1)^2
Take square root of both sides:
Plus/minus sqrt(y-5)=x-1
We want x-1>0:
Sqrt(y-5)=x-1
Add 1 on both sides:
Sqrt(y-5)+1=x
Swap x and y:
Sqrt(x-5)+1=y
x>5
y>1
Select the correct answer.
Each statement describes a transformation of the graph of y=x. Which statement correctly describes the graph of y= x - 13?
OA. It is the graph of y= x translated 13 units to the right.
OB. It is the graph of y=xwhere the slope is decreased by 13.
It is the graph of y= x translated 13 units to the left.
OD. It is the graph of y= x translated 13 units up.
ОС.
minus sign ironically makes it go to the right
because the function crosses the y axis at -13
It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of transformation, we have to compare the two equations and look for changes.
In the equation y = x - 13, we subtract 13 from the value of x.
This means that the graph of y = x is shifted 13 units downwards,
since every point on the graph has 13 subtracted from its y-coordinate.
Hence, It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
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work out the equasion 39+(−13)
Answer:
39-13=26
Step-by-step explanation:
plus(minus)=minus
please help
find 0.
Answer:
0=70!!!!!!!!!!!!!!!!!!!!!!
Subtract the second equation from the first.
8x + 3y = 14
(4x + 3y = 8)
-
O A. 6y = 22
O B. 4x = 6
O c. -6y = 6
D. 12x = 22
Please help
Answer:
B
Step-by-step explanation:
Subtracting second equation from first, term by term , gives
(8x - 4x) + (3y - 3y) = (14 - 8) , that is
4x + 0 = 6, so
4x = 6 → B
